# What is the axis of symmetry and vertex for the graph y=-2x^2+4x-5?

Feb 17, 2017

The equation of the axis of symmetry is $x = 1$ and the vertex is $\left(1 , - 3\right)$. Please see the explanation.

#### Explanation:

When given an equation of the form, $y = a {x}^{2} + b x + c$, the equation of the axis of symmetry line is:

$x = - \frac{b}{2 a}$

This is, also, h; the x coordinate of the vertex:

$h = - \frac{b}{2 a}$

The y coordinate of the vertex, k, is the value of the function evaluated at h:

$k = y \left(h\right)$

For the given equation, $a = - 2 , b = 4 \mathmr{and} c = - 5$

The equation of the axis of symmetry is:

x = -4/(2(-2)

$x = 1$

This is, also, the x coordinated of vertex:

$h = 1$

The y coordinate of the vertex is:

$k = - 2 {\left(1\right)}^{2} + 4 \left(1\right) - 5$

$k = - 3$

The vertex is $\left(1 , - 3\right)$

Here is a graph of, the function, the axis of symmetry, and the vertex.